You could give the link an extra class like class="fancybox-inline button" (supposing you where using fancybox-inline before) and then add some style rules to your themes style.css to target this link.

Yes, you should not use class=’fancybox’ (reserved for images) but class=’fancybox-inline’ for inline content. Also make sure you activate the Inline Content section on your Settings > Media admin page.

Next, adding the ‘button’ class will allow you to dedicate specific styling to the link as per example.